Sequential Sampling Based Reliability Analysis for High Dimensional Rare Events With Confidence Intervals

Analysis of rare failure events accurately is often challenging with an affordable computational cost in many engineering applications, and this is especially true for problems with high dimensional system inputs. The extremely low probabilities of occurrences for those rare events often lead to large probability estimation errors and low computational efficiency. Thus, it is vital to develop advanced probability analysis methods that are capable of providing robust estimations of rare event probabilities with narrow confidence bounds. Generally, confidence intervals of an estimator can be established based on the central limit theorem, but one of the critical obstacles is the low computational efficiency, since the widely used Monte Carlo method often requires a large number of simulation samples to derive a reasonably narrow confidence interval. This paper develops a new probability analysis approach that can be used to derive the estimates of rare event probabilities efficiently with narrow estimation bounds simultaneously for high dimensional problems. The asymptotic behaviors of the developed estimator has also been proved theoretically without imposing strong assumptions. Further, an asymptotic confidence interval is established for the developed estimator. The presented study offers important insights into the robust estimations of the probability of occurrences for rare events. The accuracy and computational efficiency of the developed technique is assessed with numerical and engineering case studies. Case study results have demonstrated that narrow bounds can be built efficiently using the developed approach, and the true values have always been located within the estimation bounds, indicating that good estimation accuracy along with a significantly improved efficiency.

Objective Reduction Using Axiomatic Design and Product-Related Dependencies: A Layout Synthesis of an Autonomous Greenhouse Case Study

Many-objective optimization problem (MaOP) is defined as optimization with more than 3 objective functions. This high number of objectives makes the comparing solutions more challenging. This holds true for design problems which are MaOPs by nature due to the inherent complexity and multifaceted nature of real-life applications. In the last decades, many strategies have attempted to overcome MaOPs such as removing objectives based on their impact on the optimization. However, from a design perspective, removing objectives could lead to an under optimal, unfeasible or unreliable design. Consequently, objective aggregation seems to be a better approach since objectives can be grouped based on design features controlled by the designers. The proposed methodology uses Axiomatic Design to decompose a system into subsystems or components, and Product-Related Dependencies Management to identify the dependencies between components and formulate the objectives. Then, these objectives are aggregated based on the subsystems found with the Axiomatic Design. The methodology, applied to the layout synthesis of an autonomous greenhouse, can trim down the number of objectives from 15 to 5. Then, using a modified non-dominated sorting genetic algorithm-II (NSGA-II) combined with the objective aggregation, we were able to increase the number of “good” concepts found from 9 to 33 out of a total of 50 obtained designs.

Engineering for Global Development: Characterizing the Discipline Through a Systematic Literature Review

Over the past 50 years, researchers have repeatedly proposed the establishment of a new interdisciplinary engineering field in Engineering for Global Development (EGD), whose analytical tools and design processes result in positive social impacts and poverty alleviation in a global development context. Within each discipline and research area, a growing body of work has sought to systematically create scientific knowledge in this area. However, a recent network analysis of Human-Centered Design plus Development research indicates that sub-communities are not collaborating at a high level and therefore the overall research agenda may lack cohesion. This paper presents a descriptive analysis of EGD research within mechanical engineering along four dimensions through a systematic literature review and secondary data analysis. Results from the review and a Latent Dirichlet Allocation model indicate EGD work in mechanical engineering draws upon research methodologies from a number of other fields and has low levels of consensus on technical terminology. These results suggest consensus in the broader interdisciplinary EGD field should be examined.

Adaptive Linear Programming Algorithm With Parameter Learning for Managing Engineering-Design Problems

The adaptive linear programming (ALP) algorithm is an extension of the sequential linear programming algorithm where nonlinear formulations are iteratively approximated as linear formulations linearized about an iteration starting point. In the ALP algorithm, heuristics are used to determine the value of a critical parameter, namely, the reduced move coefficient (RMC). The RMC defines how far to move towards the solution of iteration “n” from the starting point for iteration “n” in specifying the starting point for iteration “n+1”. The RMC choice affects the efficacy of the approximation; however, there is no mechanism of evaluating the algorithm performance with respect to the RMC value so as to improve the design efficiency and effectiveness. This limitation is addressed in this paper. In this paper, we enhance the ALP algorithm with parameter learning (ALPPL) and generalize to make the knowledge gained reusable. We propose a three-step procedure of rule-based parameter learning leading to robust solutions. An industry-inspired problem, the integrated design of a hot rolling process chain for the production of a steel rod, is used to demonstrate the implementation. The three-step procedure could be used to improve other critical parameter determinations, especially when there is a lack of mechanisms for algorithm-performance evaluation, evaluation criteria vary with problems, or heuristics are over-used.

A Method for Solving Multi-Objective Optimization Problems Containing an Infinite Number of Parameterized Objectives

Multi-objective decision making problems can sometimes involve an infinite number of objectives. In this paper, an approach is presented for solving multi-objective optimization problems containing an infinite number of parameterized objectives, termed “infinite objective optimization”. A formulation is given for infinite objective optimization problems and an approach for checking whether a Pareto frontier is a solution to this formulation is detailed. Using this approach, a new sampling based approach is developed for solving infinite objective optimization problems. The new approach is tested on several different example problems and is shown to be faster and perform better than a brute force approach.

Utility Function Derived Off-Road Vehicle Path Planning

Optimal navigation of ground vehicles in an off-road setting is a challenging task. One must accurately model the properties of the terrain and reconcile it with vehicle capabilities, while simultaneously addressing mission requirements. An important part of navigation is path planning, the selection of the route a vehicle takes between the start and end points. It is often seen that, given the starting and end points for a vehicle, the optimal path that the vehicle should take varies considerably with the mission requirements. While most commonly used algorithms use a local cost function, mission requirements are typically defined over the entire run of the vehicle. Utility theoretic methods provide a normative tool to model tradeoffs over attributes (mission requirements) that the operator cares about. It is critical therefore, that preferences embedded in the utility function influence the local cost functions used. In this paper, we provide a framework for a feedback-based method to update the parameters of the local cost-function. We do so by using a geodesic-based method for path planning given the terrain inputs, followed by a physics-based simulation of a vehicle to evaluate the attributes. These attributes are then combined into a multiattribute utility function. An optimization-based approach is used to find the parameters of the cost function that maximizes this multiattribute utility. We present our approach on a vehicle navigation example over a terrain acquired from United States Geological Survey data.

Stochastic Kriging for Crashworthiness Optimization Accounting for Simulation Noise

Vehicle crash simulations are notoriously costly and noisy. When performing crashworthiness optimization, it is therefore important to include available information to quantify the noise in the optimization. For this purpose, a stochastic kriging can be used to account for the uncertainty due to the simulation noise. It is done through the addition of a non-stationary stochastic process to the deterministic kriging formulation. This stochastic kriging, which can also be used to include the effect of random non-controllable parameters, can then be used for surrogate-based optimization. In this work, a stochastic kriging-based optimization algorithm is proposed with an infill criterion referred to as the Augmented Expected Improvement, which, unlike its deterministic counterpart the Expect Improvement, accounts for the presence of irreducible aleatory variance due to noise. One of the key novelty of the proposed algorithm stems from the approximation of the aleatory variance and its update during the optimization. The proposed approach is applied to the optimization of two problems including an analytical function and a crashwor-thiness problem where the components of an occupant restraint system of a vehicle are optimized.

Microgrid Power Management With Integrated Quality of Life Considerations

Electrification can act as a catalyst in social progress. In some communities, grid connection is not possible. As such, microgrids are a viable alternative to provide access to electricity. Yet, progress can be impacted by challenges with insufficient energy supply. In such scenarios, it is important to understand the relationships between electricity supply and social development in managing available resources. We propose a framework to relate quality of life with power management, such that progress is not hindered when available energy is insufficient. In this paper, electrical loads for pumping water, powering streetlights, and powering household devices are examined. A compromise decision support problem (cDSP) is developed to balance the produced and consumed energy. We develop a set of power management options by exploring the solution space developed from performing the cDSP, anchored in quality of life. Organizations engaged in sustainable development can select the solution most appropriate for the community. A salient feature of the framework is the versatility. The formulation can be modified for different requirements, communities, and time periods. A test problem is used to illustrate the flexibility of the approach. This framework is constructed to support decision making for microgrid operation to continue to uplift communities.

Applications of Polynomial Chaos-Based Cokriging to Simulation-Based Analysis and Design Under Uncertainty

This paper demonstrates the use of the polynomial chaos-based Cokriging (PC-Cokriging) on various simulation-based problems, namely an analytical borehole function, an ultrasonic testing (UT) case and a robust design optimization of an airfoil case. This metamodel is compared to Kriging, polynomial chaos expansion (PCE), polynomial chaos-based Kriging (PC-Kriging) and Cokriging. The PC-Cokriging model is a multi-variate variant of PC-Kriging and its construction is similar to Cokriging. For the borehole function, the PC-Cokriging requires only three high-fidelity samples to accurately capture the global accuracy of the function. For the UT case, it requires 20 points. Sensitivity analysis is performed for the UT case showing that the F-number has negligible effect on the output response. For the robust design case, a 75 and 31 drag count reduction is reported on the mean and standard deviation of the drag coefficient, respectively, when compared to the baseline shape.

Surrogate Model Assisted Lithium-Ion Battery Co-Design for Fast Charging and Cycle Life Performances

As one of the significant enablers of portable devices and electric vehicles, lithium-ion batteries are drawing much attention for their high energy density and low self-discharging rate. A major hindrance to their further development has been the “range anxiety”, that fast-charging of Li-ion battery is not attainable without sacrificing battery life. In the past, much effort has been carried out to resolve such a problem by either improve the battery design or optimize the charging/discharging protocols, while limited work has been done to address the problem simultaneously, or through a control co-design framework, for a system-level optimum. The control co-design framework is ideal for lithium-ion batteries due to the strong coupling effects between battery design and control optimization. The integration of such coupling effects can lead to improved performances as compared with traditional sequential optimization approaches. However, the challenge of implementing such a co-design framework has been updating the dynamics efficiently for design variations. In this study, we optimize the charging time and cycle life of a lithium-ion battery as a control co-design problem. Specifically, the anode volume fraction and particle size, and the corresponding charging current profile are optimized for a minimum charging time with health-management considerations. The battery is modeled as a coupled electro-thermal-aging dynamical system. The design-dependent dynamics is parameterized thru a Gaussian Processes model, that has been trained with high-fidelity multiphysics simulation samples. A nested co-design approach was implemented using direct transcription, which achieves a better performance than the sequential design approach.